### 112.5.5 Cohomology

Papers discussing cohomology of sheaves on algebraic stacks.

Olsson:

*Sheaves on Artin stacks*[olsson_sheaves]This paper develops the theory of quasi-coherent and constructible sheaves proving basic cohomological properties. This paper corrects a mistake in [LM-B] in the functoriality of the lisse-étale site. The cotangent complex is constructed. In addition, the following theorems are proved: Grothendieck's Fundamental Theorem for proper morphisms, Grothendieck's Existence Theorem, Zariski's Connectedness Theorem and finiteness theorem for proper pushforwards of coherent and constructible sheaves.

Behrend:

*Derived $l$-adic categories for algebraic stacks*[behrend_derived]Proves the Lefschetz trace formula for algebraic stacks.

Behrend:

*Cohomology of stacks*[behrend_cohomology]Defines the de Rham cohomology for differentiable stacks and singular cohomology for topological stacks.

Faltings:

*Finiteness of coherent cohomology for proper fppf stacks*[faltings_finiteness]Proves coherence for direct images of coherent sheaves for proper morphisms.

Abramovich, Corti, Vistoli:

*Twisted bundles and admissible covers*[acv]The appendix contains the proper base change theorem for étale cohomology for tame Deligne-Mumford stacks.

## Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like `$\pi$`

). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

## Comments (0)

There are also: